﻿54 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  molecules. 
  Denoting 
  the 
  angular 
  velocity 
  of 
  the 
  electron 
  in 
  

   the 
  three-electron 
  atom, 
  which 
  we 
  may 
  call 
  hydrogen, 
  by 
  o>, 
  

   the 
  linear 
  velocity 
  by 
  </, 
  velocity 
  of 
  light 
  by 
  c, 
  the 
  radius 
  

   of 
  the 
  orbit 
  by 
  a, 
  the 
  distance 
  between 
  the 
  two 
  atoms 
  in 
  

   the 
  H 
  2 
  molecule 
  by 
  r 
  = 
  av, 
  the 
  ratio 
  q/c 
  = 
  /3, 
  w 
  T 
  e 
  have 
  the 
  

   evident 
  relations 
  

  

  aco 
  rco 
  five 
  

  

  B= 
  — 
  , 
  pc= 
  — 
  , 
  or 
  o)= 
  , 
  

  

  c 
  c 
  r 
  

  

  from 
  which 
  the 
  wave-length 
  of 
  a 
  wave 
  travelling 
  with 
  the 
  

   velocity 
  of 
  light, 
  having 
  the 
  same 
  period 
  as 
  the 
  electrons 
  in 
  

   their 
  orbits, 
  and 
  the 
  frequency 
  are 
  found 
  to 
  be 
  

  

  . 
  2lTV 
  , 
  J3VQ 
  

  

  X= 
  -7s— 
  and 
  ?i= 
  '- 
  — 
  -, 
  

   /3v 
  2irr 
  

  

  It 
  has 
  been 
  shown 
  that 
  the 
  product 
  fiv 
  is 
  nearly 
  the 
  same 
  

   for 
  all 
  the 
  diatomic 
  molecules, 
  being 
  2'66 
  for 
  atoms 
  with 
  

   a 
  single 
  ring 
  of 
  three 
  electrons. 
  Hence 
  the 
  only 
  factor 
  in 
  

   the 
  wave-length 
  or 
  the 
  frequency 
  that 
  is 
  uncertain 
  is 
  the 
  

   distance 
  r 
  between 
  the 
  two 
  atoms. 
  In 
  round 
  numbers 
  it 
  is 
  

   usual 
  to 
  take 
  the 
  dimensions 
  of 
  a 
  molecule 
  as 
  10~ 
  8 
  cm 
  , 
  and 
  

   this 
  is 
  the 
  approximate 
  value 
  of 
  r. 
  This 
  value 
  of 
  r 
  makes 
  

   the 
  fundamental 
  frequency 
  of 
  the 
  electrons 
  in 
  their 
  orbits 
  

   1270 
  XlO 
  15 
  , 
  and 
  the 
  wave-length 
  2'36 
  x 
  10~ 
  8 
  cm. 
  Very 
  

   short 
  ultra-violet 
  waves 
  of 
  light 
  have 
  a 
  frequency 
  and 
  

   wave-length 
  1*5 
  x 
  10 
  15 
  and 
  2000 
  X 
  10~ 
  8 
  respectively. 
  The 
  

   frequency 
  of 
  the 
  electron 
  is, 
  therefore, 
  847 
  times 
  greater 
  than 
  

   short 
  ultra-violet 
  waves, 
  and 
  the 
  wave-length 
  correspondingly 
  

   shorter. 
  

  

  The 
  size 
  of 
  the 
  molecule, 
  10 
  ~ 
  8 
  , 
  is 
  obtained 
  by 
  one 
  method 
  

   from 
  the 
  kinetic 
  theoiy 
  of 
  gases 
  by 
  considerations 
  of 
  the 
  

   mean 
  free 
  paths 
  of 
  the 
  molecules. 
  It 
  is 
  quite 
  conceivable 
  

   that 
  by 
  this 
  means 
  larger 
  values 
  would 
  be 
  obtained 
  than 
  

   would 
  be 
  the 
  case 
  if 
  we 
  could 
  directly 
  measure 
  the 
  distance 
  

   between 
  the 
  two 
  atoms 
  of 
  the 
  molecule. 
  For 
  the 
  reasons 
  

   above 
  given 
  that 
  the 
  parts 
  of 
  adjacent 
  molecules 
  should 
  be 
  

   considerably 
  further 
  apart 
  than 
  the 
  atoms 
  of 
  the 
  molecule 
  

   itself, 
  it 
  seems 
  probable 
  that 
  the 
  separation 
  between 
  the 
  two 
  

   atoms 
  of 
  the 
  diatomic 
  molecule 
  is 
  somewhat 
  less 
  than 
  10" 
  8 
  cm. 
  

   If 
  so, 
  the 
  wave-length 
  computed 
  above 
  would 
  be 
  shorter 
  

   still, 
  and 
  the 
  frequency 
  greater. 
  

  

  The 
  wave-length 
  and 
  frequency 
  of 
  the 
  X-rays 
  has 
  recently 
  

   been 
  measured, 
  or 
  computed 
  from 
  measurements 
  of 
  the 
  

   diffraction 
  patterns 
  obtained 
  from 
  crystals 
  *, 
  to 
  be 
  from 
  

   \=V21 
  to 
  483 
  xlO" 
  9 
  cm. 
  and 
  n 
  = 
  2'36 
  to 
  -621 
  x 
  10 
  19 
  cm. 
  

  

  * 
  Laue, 
  Friedrich, 
  and 
  Knipping, 
  Milnch. 
  Ber. 
  pp. 
  303-322 
  (1912). 
  

  

  